A frequency spectrum plot showing intermodulation between two injected signals at 270 and 275 MHz (the large spikes). Visible intermodulation products are seen as small spurs at 280 MHz and 265 MHz.

Intermodulation (IM) or intermodulation distortion (IMD) is the amplitude modulation of signals containing two or more different frequencies in a system with nonlinearities. The intermodulation between each frequency component will form additional signals at frequencies that are not just at harmonic frequencies (integermultiples) of either, but also at the sum and difference frequencies of the original frequencies and at multiples of those sum and difference frequencies.

Intermodulation is caused by non-linear behaviour of the signal processing (physical equipment or even algorithms) being used. The theoretical outcome of these non-linearities can be calculated by generating a Volterra series of the characteristic, while the usual approximation of those non-linearities is obtained by generating a Taylor series.[citation needed]

Practically all audio equipment has some non-linearity, so it will exhibit some amount of IMD, which however may be low enough to be imperceptible by humans. Due to the characteristics of the human auditory system, the same percentual amount of IM is perceived as more bothersome than the same amount of harmonic distortion.[1][2] Intermodulation is also rarely desirable in radio, as it creates unwanted spurious emissions, often in the form of sidebands. For radio transmissions this increases the occupied bandwidth, leading to adjacent channel interference, which can reduce audio clarity or increase spectrum usage. It should not be confused with harmonic distortion (which has common musical applications), nor with intentional modulation (such as a frequency mixer in superheterodyne receivers) where signals to be modulated are presented to an intentional nonlinear element (multiplied) (see non-linearmixers such as mixer diodes and even single-transistor oscillator-mixer circuits). In audio, the intermodulation products are nonharmonically related to the input frequencies and therefore "off-key" with respect to the common Western musical scale.

A linear system cannot produce intermodulation. If the input of a linear time-invariant system is a signal of a single frequency, then the output is a signal of the same frequency; only the amplitude and phase can differ from the input signal. However, non-linear systems generate harmonics, meaning that if the input of a non-linear system is a signal of a single frequency, then the output is a signal which includes a number of integer multiples of the input frequency; (i.e. some of ).

Intermodulation occurs when the input to a non-linear system is composed of two or more frequencies. Consider an input signal that contains three frequency components at, , and ; which may be expressed as

where the and are the amplitudes and phases of the three components, respectively.

will contain the three frequencies of the input signal, , , and (which are known as the fundamental frequencies), as well as a number of linear combinations of the fundamental frequencies, each of the form

where , , and are arbitrary integers which can assume positive or negative values. These are the intermodulation products (or IMPs).

In general, each of these frequency components will have a different amplitude and phase, which depends on the specific non-linear function being used, and also on the amplitudes and phases of the original input components.

More generally, given an input signal containing an arbitrary number of frequency components , the output signal will contain a number of frequency components, each of which may be described by

In many radio and audio applications, odd-order IMPs are of most interest, as they fall within the vicinity of the original frequency components, and may therefore interfere with the desired behaviour.

As explained in a previous section, intermodulation can only occur in non-linear systems. Non-linear systems are generally composed of active components, meaning that the components must be biased with an external power source which is not the input signal (i.e. the active components must be "turned on"). Passive intermodulation (PIM), however, occurs in passive devices (which may include cables, antennas etc.) that are subjected to two or more high power tones. The PIM product is the result of the two (or more) high power tones mixing at device nonlinearities such as junctions of dissimilar metals, metal-oxide junctions and even loose connectors. The higher the signal amplitudes, the more pronounced the effect of the nonlinearities, and the more prominent the intermodulation that occurs - even though upon initial inspection, the system would appear to be linear and unable to generate intermodulation.

Ferromagnetic materials are the most common materials to avoid and include ferrites, nickel, (including nickel plating) and steels (including some stainless steels.) These materials exhibit hysteresis when exposed to reversing magnetic fields resulting in PIM generation.

PIM can also be generated in components with manufacturing or workmanship defects, such as cold or cracked solder joints or poorly made mechanical contacts. If these defects are exposed to high RF currents, PIM can be generated. As a result, RF equipment manufacturers perform factory PIM tests on components, to eliminate PIM caused by these design and manufacturing defects.

In the field, PIM can be caused by components that were damaged in transit to the cell site, installation workmanship issues and by external PIM sources. Some of these include:

Contaminated surfaces or contacts due to dirt, dust, moisture or oxidation.

Inconsistent metal-to-metal contact between RF connector surfaces caused by any of the following:

Trapped dielectric materials (adhesives, foam, etc.), cracks or distortions at the end of the outer conductor of coaxial cables, often caused by overtightening the back nut during installation, solid inner conductors distorted in the preparation process, hollow inner conductors excessively enlarged or made oval during the preparation process.

PIM can also occur in connectors, or when conductors made of two galvanically unmatched metals come in contact with each other.

IEC 62037 is the international standard for PIM testing and gives specific details as to PIM measurement setups. The standard specifies the use of two +43 dBm (20W) tones for the test signals for PIM testing. This power level has been used by RF equipment manufacturers for more than a decade to establish PASS / FAIL specifications for RF components.

Slew-induced distortion (SID) can produce intermodulation distortion (IMD) when the first signal is slewing (changing voltage) at the limit of the amplifier's power bandwidth product. This induces an effective reduction in gain, partially amplitude-modulating the second signal. If SID only occurs for a portion of the signal, it is called "transient" intermodulation distortion.[3]

Intermodulation distortion in audio is usually specified as the Root Mean Square (RMS) value of the various sum-and-difference signals as a percentage of the original signal's RMS voltage, although it may be specified in terms of individual component strengths, in decibels, as is common with RF work. Audio IMD standard tests include SMPTE standard RP120-1994[3] where two signals (at 60 Hz and 7 kHz, with 4:1 amplitude ratios) are used for the test; many other standards (such as DIN, CCIF) use other frequencies and amplitude ratios. Opinion varies over the ideal ratio of test frequencies (e.g. 3:4,[4] or almost -but not exactly - 3:1 for example).

After feeding the equipment under test with low distortion input sinewaves, the output distortion can be measured by using an electronic filter to remove the original frequencies, or spectral analysis may be made using Fourier Transformations in software or a dedicated spectrum analyser, or when determining intermodulation effects in communications equipment, may be made using the receiver under test itself.